Hey Gary :) Nice to see you around
For this question, we want to use logarithmic rules to write the expression as a single logarithm.
Using the rule [tex] log_{b} ( M^{k} ) = k * log_{b} M[/tex] , we can simplify
[tex] 3log_{b} q[/tex] to [tex]log_{b} ( q^{3} )[/tex] . We can also simplify [tex] 6log_{b}(v) [/tex] to [tex] log_{b}( v^{6}) [/tex] .
So, we have [tex]log_{b} ( q^{3} )[/tex] + [tex] log_{b}( v^{6}) [/tex].
Another logarithmic rule is:
[tex] log_{b}(M*N) = log_{b} M + log_{b} N
[/tex]
Using this rule, we can use the logs we have calculated and change them to:
[tex] log_{b}( q^{3} v^{6}) [/tex]
This matches answer choice A.
Hope this helps! Feel free to contact me with any questions.
